Shyam visited Ram during his brief vacation. In the mornings they both

Question

Shyam visited Ram during his brief vacation. In the mornings they both would go for yoga. In the evenings they would play tennis. To have more fun, they indulged only on one activity per day, i.e either they went for yoga or played tennis each day. There were days when they were lazy and stayed home all day long. There were 24 mornings when they did nothing, 14 evening when they stayed at home and total of 22 days when they did yoga or played tennis. For how many days Shaym stayed with Ram?

A. 20
B. 25
C. 30
D. 35
E. 40

A. 20
B. 25
C. 30
D. 35
E. 40

Palak74 · Accepted Answer

Assume total Days together were X 
They did yoga on X-24 Number of days 
They played Tennis on X-14 Number of days
Total number of days they did the two activities is 22 
Thus , 
(X-24)+(X-14)=22
Solving the above equation 
X=30 Days

azamatboden · Answer

T = only tennis
N = nothing
Y = only yoga

24 = T+N
14= Y+ N
22 = Y + T

a set of 3 equations after which you can find that T = 16, Y=6, N= 8 --> Total = 30 days

nick1816 · Answer

Each day they had 2 sessions. In each session either they went for yoga or played tennis or took rest.

Total sessions they had = 24+14+22=60

Total number of days = 60/2 = 30

krushal95 · Answer

Each day they had 2 sessions. In each session either they went for yoga or played tennis or took rest.

Total sessions they had = 24+14+22=60

Total number of days = 60/2 = 30

--> how did you get the total number of days=60/2=30 ?

ansarose · Answer

Aren't we dividing by 2 to get combinations of two activities from the total no sessions , so as to get the total no of days from these sessions? 
   Posted from my mobile device

philipssonicare · Answer

This has been posted to overlapping sets. The algebraic approach makes sense, but how can this be solved using a matrix or venn diagram?

udaypratapsingh99 · Answer

Maximum possible Yoga days = 14
Maximum possible Tennis days = 24
Maximum possible total days (if there were no lazy stay home day) = 14+28 = 38

Yoga+Tennis days = 22

Lazy stay home days =  (38 - 22)/2   = 8

Total days = 22 + 8 = 30

C is Correct

LucienH · Answer

total number of days would be:

# of mornings spent at home + # of nights spent at home + the number of days where they did nothing

We are given that they spent 24 mornings at home and 14 nights at home, but these values both include the number of days they did nothing

Let x = # of days they did nothing

22 + x = 24 + 14 - x

Alternatively, you could think of this as:

# of days they Didn't rest = 22 = 24 + 14 - 2x (since you double count the number of days they did nothing)

Both ways work and yield x = 8 days, 
meaning that the # of days they rested was 8 and that the total number of days they spent together was 22 + 8 = 30

samarpan.g28 · Answer

Consider the total number of days as T, out of which, x mornings are used for yoga and y evenings are used for tennis. So T-21=x and T-14=y. Now, x+y=22 or, T-24+T-14=22 or, 2T=60 or, T=30. Option C is correct.

HarshavardhanR · Answer

Went for Yoga 
 Did not go for Yoga 
 Total 
 
  Went for Tennis 
 0 
 b

Did not go for Tennis 
 a 
 24 - b 
 14 
 
  Total 
 a 
 24 
 a+24

- They indulged only on one activity per day
 
=> 0 days of both Tennis and Yoga (as shown)

-  There were 24 mornings when they did nothing

=> Days on which they did not go for Yoga = 24

- 14 evening when they stayed at home

=> Days on which they did not go for Tennis = 14

- Total of 22 days when they did yoga or played tennis

=> a + b = 22

(1) a + b = 22

Observe the table.

(2) a + 24 - b = 14

=> a - b = -10

From (1) and (2)

a = 6 
 b = 16

Total number of days Shyam stayed with Ram = a + 24 = 6 + 24 = 30 days. Choice C.

---
Harsha

KarishmaB · Answer

Here is the Venn diagram solution:

Shyam visited Ram during his brief vacation. In the mornings they both

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	Went for Yoga	Did not go for Yoga	Total
Went for Tennis	0	b
Did not go for Tennis	a	24 - b	14
Total	a	24	a+24

GMAT Problem Solving (PS) Questions

Shyam visited Ram during his brief vacation. In the mornings they both

Prep Toolkit

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